Subgroups — C₃₁×(C₁₁⋊C₅)⋊Dic₅ #46802016

Order 34100.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₁×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₁×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₁×Dic₁₁⋊C₅	—	5	1	no	maximal
4	C₃₁×Dic₅₅	C₅	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×C₁₁⋊C₅	—	2	2	no	—
6	C₂×C₃₁×C₁₁⋊C₅	D₅	1	1	yes	characteristic
7	C₂×C₅×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic
8	C₅×Dic₅×C₃₁	—	11	1	no	maximal, Hall
9	C₅×C₁₁×C₃₁	C₄×C₅	1	1	yes	characteristic, complemented
10	C₃₁×C₁₁⋊C₅	—	2	2	no	—
11	C₃₁×C₁₁⋊C₅	Dic₅	1	1	yes	characteristic, complemented
12	C₂×C₅²×C₃₁	—	11	1	no	—
13	C₃₁×Dic₁₁	—	5	1	no	Hall
14	(C₁₁⋊C₅)⋊Dic₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₅²×C₃₁	—	11	1	no	Hall
16	C₂×C₁₁×C₃₁	C₅×D₅	1	1	yes	characteristic
17	C₄×C₅×C₃₁	—	55	1	no	—
18	Dic₅×C₃₁	—	11	1	no	—
19	C₂×C₅×C₁₁⋊C₅	C₂×C₃₁	1	1	yes	characteristic
20	C₁₁×C₃₁	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₃₁	—	11	1	no	—
22	C₂×C₅×C₃₁	—	22	2	no	—
23	C₂×C₅×C₃₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic
24	C₅×C₁₁⋊C₅	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
25	Dic₅₅	C₅×C₃₁	1	1	yes	characteristic, complemented
26	Dic₁₁⋊C₅	—	5	1	no	—
27	C₅×C₃₁	—	11	1	no	—
28	C₅×C₃₁	—	22	2	no	—
29	C₅×C₃₁	Dic₁₁⋊C₅	1	1	yes	characteristic, complemented
30	C₄×C₃₁	—	55	1	no	Hall
31	C₂×C₅×C₁₁	C₂×C₅×C₃₁	1	1	yes	characteristic
32	C₂×C₁₁⋊C₅	—	2	2	no	—
33	C₂×C₁₁⋊C₅	D₅×C₃₁	1	1	yes	characteristic
34	C₅×Dic₅	—	11	1	no	Hall
35	C₂×C₃₁	C₅⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
36	C₅×C₁₁	C₄×C₅×C₃₁	1	1	yes	characteristic, complemented
37	C₁₁⋊C₅	—	2	2	no	—
38	C₁₁⋊C₅	Dic₅×C₃₁	1	1	yes	characteristic, complemented
39	C₂×C₅²	—	11	1	no	—
40	Dic₁₁	—	5	1	no	Hall
41	C₃₁	(C₁₁⋊C₅)⋊Dic₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₅²	—	11	1	no	Sylow
43	C₂×C₁₁	C₅×D₅×C₃₁	1	1	yes	characteristic
44	C₄×C₅	—	55	1	no	—
45	Dic₅	—	11	1	no	—
46	C₁₁	C₅×Dic₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₅	—	11	1	no	—
48	C₂×C₅	—	22	2	no	—
49	C₂×C₅	C₃₁×AGL(1,𝔽₁₁)	1	1	yes	characteristic
50	C₅	—	11	1	no	—
51	C₅	—	22	2	no	—
52	C₅	C₃₁×Dic₁₁⋊C₅	1	1	yes	characteristic, complemented
53	C₄	—	55	1	no	Sylow
54	C₂	C₃₁×C₅⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃₁	C₅⋊AGL(1,𝔽₁₁)
commutator, hypocenter	C₅×C₁₁	C₄×C₅×C₃₁
Frattini	C₂	C₃₁×C₅⋊AGL(1,𝔽₁₁)
Fitting, socle	C₂×C₅×C₁₁×C₃₁	C₂×C₅
prime radical	C₂×C₅×C₃₁×C₁₁⋊C₅	C₂
cosocle	C₂×C₅×C₁₁	C₂×C₅×C₃₁
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂×C₃₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅×C₃₁×C₁₁⋊C₅	C₄	semidirect
4. C₃₁×Dic₅₅	C₅	semidirect
9. C₅×C₁₁×C₃₁	C₄×C₅	semidirect
11. C₃₁×C₁₁⋊C₅	Dic₅	semidirect
14. (C₁₁⋊C₅)⋊Dic₅	C₃₁	direct (N × H)
20. C₁₁×C₃₁	C₅×Dic₅	semidirect
24. C₅×C₁₁⋊C₅	C₄×C₃₁	semidirect
25. Dic₅₅	C₅×C₃₁	semidirect
29. C₅×C₃₁	Dic₁₁⋊C₅	semidirect
36. C₅×C₁₁	C₄×C₅×C₃₁	semidirect
38. C₁₁⋊C₅	Dic₅×C₃₁	semidirect
41. C₃₁	(C₁₁⋊C₅)⋊Dic₅	direct (N × H)
46. C₁₁	C₅×Dic₅×C₃₁	semidirect
52. C₅	C₃₁×Dic₁₁⋊C₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×C₃₁×C₁₁⋊C₅	2
C₃₁×Dic₁₁⋊C₅	5
C₃₁×Dic₅₅	5
C₅×Dic₅×C₃₁	11
(C₁₁⋊C₅)⋊Dic₅	31

Subgroups — C31×(C11⋊C5)⋊Dic5 #46802016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×(C₁₁⋊C₅)⋊Dic₅ #46802016